This invention relates to puzzle pieces which have either a nature to tile non-periodic geometric designs against a flat surface or to spatially interrelate as an integrated and coherent three-dimensional structure.
The simpler of the piece shapes comprises and conforms closely to a polyhedron having six surfaces, one of which surfaces is a concave polygon of five equal sides. Each of the other five surfaces borders a different one of the five sides and together make five dihedral angles with the polygon. Four of these dihedrals measure about 63 degrees each. The fifth is about half of that measure and is located opposite the two divergent sides of the polygon.
The other piece shape is in ways similar to the first and conforms closely to a lengthier polyhedron of two more surfaces than the earlier polyhedron. The six surfaces described for that earlier polyhedron are represented in the second polyhedron, more or less preserving all angular relationships. The second polyhedron does differ though in that the surfaces which preserve the corresponding fifth dihedral angle are, by comparison, expanded lengthwise and extended widthwise at midsections while the two surfaces corresponding opposite of this angle are seen to be non-adjacent to include between them instead the seventh and eighth surfaces, these latter four surfaces making, furthermore, parallel pairs of surfaces.